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If ln((e-1)e^(xy) +x^2)=x^2+y^2 then ((d...

If `ln((e-1)e^(xy) +x^2)=x^2+y^2` then `((dy)/(dx))_(1,0)` is equal to

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To solve the problem, we need to differentiate the given equation and find the value of \(\frac{dy}{dx}\) at the point (1, 0). Given: \[ \ln((e-1)e^{xy} + x^2) = x^2 + y^2 \] ### Step 1: Exponentiate both sides ...
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CENGAGE ENGLISH-DIFFERENTIATION-Execrises
  1. "Let "e^(y)=(sqrt(1+alpha)+sqrt(1-alpha))/(sqrt(1+alpha)-sqrt(1-alpha)...

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  2. The derivative of tan^(-1)((sqrt(1+x^2)-1)/x) with respect to tan^(-1)...

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  3. If ln((e-1)e^(xy) +x^2)=x^2+y^2 then ((dy)/(dx))(1,0) is equal to

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  4. If y=(x^x)^x then (dy)/(dx) is

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  5. The first derivative of the function [cos^(-1)(sin sqrt((1+x)/2))+x^x]...

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  6. f(x)=x^x , x in (0,oo) and let g(x) be inverse of f(x) , then g(x)'...

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  7. If y=a x^(n+1)+b x^(-n),t h e nx^2(d^2y)/(dx^2) is equal to n(n-1)y (b...

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  8. If y=a x^(n+1)+b x^(-n),t h e nx^2(d^2y)/(dx^2) is equal to n(n-1)y (b...

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  9. Suppose f(x)=e^(ax)+e^(bx)," where " a ne b, and that f''(x) -2f'(x)-1...

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  10. (d^(20)y)/(dx^(20))(2cosxcos3x)i se q u a l to a)2^(20)(cos2x-2^(20)o...

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  11. (d^n)/(dx^n)(logx)= ((n-1)!)/(x^n) (b) (n !)/(x^n) ((n-2)!)/(x^n) (d...

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  12. "If "y= xlog ((x)/(a+bx))," then "x^(3)(d^(2)y)/(dx^(2))=

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  13. If a x^2+2h x y+b y^2=1,t h e n(d^(2y))/(dx^2) is (h^2-a b)/((h x+b y)...

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  14. "If "y^(1//m)=(x+sqrt(1+x^(2)))," then "(1+x^(2))y(2)+xy(1) is (where ...

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  15. If ( sin x) (cos y) = 1//2, then d^(2)y//dx^(2) at (pi//4, pi//4) is

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  16. A function f satisfies the condition f(x)=f'(x)+f''(x)+f'''(x)+…, wher...

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  17. Let f(x) be a polynomial of degree 3 such that f(3)=1, f'(3)=-1, f''(3...

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  18. If y^2=a x^2+b x+c , then y^3(d^2y)/(dx^2) is (a) a constant (b) a fun...

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  19. "If "y= sin x +e^(x)," then "(d^(2)x)/(dy^(2))=

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  20. If f''(x) =- f(x) and g(x) = f'(x) and F(x)=(f((x)/(2)))^(2)+(g((x)/(2...

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